The invention refers to an apparatus of the in the introduction of claim 1 described type. From the U.S. patent application Ser. No. 1,556,471 a similar apparatus is known. This well-known apparatus is suitable for sharpening the edges of instruments with outer cutting edges. However, it is not possible to sharpen instruments with inner, curved cutting edges of different cutting angles. The reproduction of the outer grinding angles is also doubtful, as it is not stated where to place the cutting edge on the grinding disk during the grinding process. The requirements of hygiene in connection with e.g. dental intruments cannot be met by this well-known technique, either. The purpose of the invention is to present an apparatus of the above mentioned well-known type, but by which the disadvantages of the well-known technique are rectified.